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authorKatolaZ <katolaz@yahoo.it>2015-10-19 16:30:12 +0100
committerKatolaZ <katolaz@yahoo.it>2015-10-19 16:30:12 +0100
commita86962cbfd0321387c920a04188512d0de2f3036 (patch)
treeb6c0d31342f7af9d605ee83cfffe251554a307d4 /doc/html/mammult_docsu21.html
parentdf8386f75b0538075d72d52693836bb8878f505b (diff)
First commit of MAMMULT documentation
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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+<head><title>1.1.4.0 avg_edge_overlap.py</title>
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+>
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+ <h5 class="subsubsectionHead"><a
+ id="x24-230001.1.4"></a><span
+class="cmtt-10x-x-109">avg</span><span
+class="cmtt-10x-x-109">_edge</span><span
+class="cmtt-10x-x-109">_overlap.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">avg</span><span
+class="cmbx-10x-x-109">_edge</span><span
+class="cmbx-10x-x-109">_overlap.py </span>- compute the average edge overlap of a multiplex.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">avg</span><span
+class="cmbx-10x-x-109">_edge</span><span
+class="cmbx-10x-x-109">_overlap.py </span><span
+class="cmmi-10x-x-109">&#x003C;</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">&#x003E; </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109">&#x003C;</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">&#x003E;</span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 29--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 29--><p class="indent" > Compute and print on output the average edge overlap
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc4x.png" alt=" &sum; &sum; &sum; [&alpha;]
+ &lowast; &sum;--&sum;-i--j&#x003E;i---&alpha;aij----
+&omega; = i j&#x003E;i(1&minus; &delta; &sum; [&alpha;])
+ 0, &alpha; aij
+" class="math-display" ></center></td></tr></table>
+<!--l. 29--><p class="nopar" >
+<!--l. 29--><p class="noindent" >i.e., the expected <span
+class="cmti-10x-x-109">number </span>of layers on which an edge of the multiplex exists, and
+the corresponding normalised quantity:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc5x.png" alt=" &sum; &sum; &sum; a[&alpha;]
+&omega; = ---&sum;--&sum;i--j&#x003E;i--&alpha;--ij-----
+ M i j&#x003E;i(1&minus; &delta;0,&sum;&alpha; a[i&alpha;j] )
+" class="math-display" ></center></td></tr></table>
+<!--l. 29--><p class="nopar" >
+<!--l. 29--><p class="noindent" >that is the expected <span
+class="cmti-10x-x-109">fraction </span>of layers on which an edge of the multiplex is
+present.
+<!--l. 29--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 29--><p class="indent" > &#x00A0; <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 29--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 38--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 38--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a single line, in the format:
+<!--l. 38--><p class="indent" > &#x00A0; <span
+class="cmti-10x-x-109">omega</span><span
+class="cmti-10x-x-109">_star omega</span>
+<!--l. 38--><p class="noindent" >where <span
+class="cmti-10x-x-109">omega</span><span
+class="cmti-10x-x-109">_star </span>and <span
+class="cmti-10x-x-109">omega </span>are, respectively, the expected number and fraction
+of layers in which an edge is present.
+<!--l. 42--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 42--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, &#8220;Structural measures for multiplex
+networks&#8221;, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">89</span>, 032804 (2014).
+<!--l. 42--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a>
+<!--l. 42--><p class="indent" > L. Lacasa, V. Nicosia, V. Latora, <span
+class="cmti-10x-x-109">&#8220;Network structure of multivariate time</span>
+<span
+class="cmti-10x-x-109">series&#8221;</span>, accepted for publication in Scientific Reports, arxiv:1408.0925
+(2015).
+<!--l. 42--><p class="indent" > Link to paper: <a
+href="http://arxiv.org/abs/1408.0925" class="url" ><span
+class="cmtt-10x-x-109">http://arxiv.org/abs/1408.0925</span></a>
+
+
+
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